Knot Mosaics for the 61 Knot

For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized.

The mosaic of the 61 knot given in the table has the mosaic number and tile number realized, but the crossing number of this knot cannot be realized on a 5-mosaic. The crossing number is first realized on a 6-mosaic. Below are the relevant mosaics.

61 with mosaic and tile numbers realized
61 with crossing number realized

Back to the Knot Mosaic Table

References:

Heap, A.; Knowles, D. Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6; Involve 2019, 12.
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Knot Mosaics For Prime Knots with Crossing Number 10 or Less; in preparation.
Lee, H.; Ludwig, L.; Paat, J.; Peiffer, A. Knot Mosaic Tabulation; Involve 2018, 11.
Ludwig, L.; Evans, E. An Infinite Family of Knots Whose Mosaic Number Is Realized in Non-reduce Projections; J. Knot Theory Ramif. 2013, 22.

[Back to Top]